What are the divisors of 4063?

1, 17, 239, 4063

There is a total of 4 positive divisors.
The sum of these divisors is 4320.
The arithmetic mean is 1080.

4 odd divisors

1, 17, 239, 4063

How to compute the divisors of 4063?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 4063 by each of the numbers from 1 to 4063 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

4063 / 1 = 4063 (the remainder is 0, so 1 is a divisor of 4063)
4063 / 2 = 2031.5 (the remainder is 1, so 2 is not a divisor of 4063)
4063 / 3 = 1354.3333333333 (the remainder is 1, so 3 is not a divisor of 4063)
...
4063 / 4062 = 1.0002461841457 (the remainder is 1, so 4062 is not a divisor of 4063)
4063 / 4063 = 1 (the remainder is 0, so 4063 is a divisor of 4063)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 4063 (i.e. 63.741666121933). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

4063 / 1 = 4063 (the remainder is 0, so 1 and 4063 are divisors of 4063)
4063 / 2 = 2031.5 (the remainder is 1, so 2 is not a divisor of 4063)
4063 / 3 = 1354.3333333333 (the remainder is 1, so 3 is not a divisor of 4063)
...
4063 / 62 = 65.532258064516 (the remainder is 33, so 62 is not a divisor of 4063)
4063 / 63 = 64.492063492063 (the remainder is 31, so 63 is not a divisor of 4063)